Second Order Ideal-Ward Continuity

The main aim of the paper is to introduce a concept of second order ideal-ward continuity in the sense that a function f is second order ideal-ward continuous if I-limn→∞Δ2f(xn)=0 whenever I-limn→∞Δ2xn=0 and a concept of second order ideal-ward compactness in the sense that a subset E of R is second order ideal-ward compact if any sequence x=(xn) of points in E has a subsequence z=(zk)=(xnk) of the sequence x such that I-limk→∞Δ2zk=0 where Δ2zk=zk+2-2zk+1+zk. We investigate the impact of changing the definition of convergence of sequences on the structure of ideal-ward continuity in the sense of second order ideal-ward continuity and compactness of sets in the sense of second order ideal-ward compactness and prove related theorems